import matplotlib.pyplot as plt
import numpy as np

fig = plt.figure(figsize=(6, 6))
ax = plt.gca()
t = np.linspace(0.1, 1, 100)
r=(1+np.tan(t)**2)**3/2*50*t*np.sin(t)*np.cos(t)**2

plt.plot(t, r, color='blue', linewidth=2, label='ellipse')
# plt.xlabel('x')
# plt.ylabel('y')
# plt.ylim(-1, 30)
# plt.xlim(-15, 16)
ax.grid()
plt.show()
pass
